HYPERBOLIC MODEL OF THE ADDITION-DILUTION METHOD IN QUANTITATIVE X-RAY-FLUORESCENCE ANALYSIS

A mathematical model based on a combination of the total addition meth od (TAM) and limit dilution method (LDM) is proposed. The model shows the hyperbolic behaviour of the experimental data when the X-ray fluor escence intensities are represented versus the addition-dilution facto r [(1-f(n))/f(n)]. The equation obtained for the chemical system can b e split into two terms, which relate directly to the processes of addi tion of the standard and dilution of the unknown. This equation fits m athematically to a hyperbolic function from which physical parameters and data of analytical interest are obtained for the samples studied. In the proposed model, some parameters are defined which are equivalen t to the fluorescence intensity of the analyte in the normalised sampl e (I-i(s)), in the standard (I-i(p)) and the corrected intensity (I-i( sc)) respectively. These parameters allow determination of the analyte concentration in an unknown and a suitable algorithm is proposed for their calculation. The proposed model is applied to the determination of Zn, Ti and Zr in a synthetic sample, prepared by homogenising the r espective metal oxides. The results are in complete agreement with the contents which suggests a good correction of the strong interelement effects typical at these levels of concentration as is demonstrated by a low error in an interval of 0.7-1.2%.